Magnetic resonance imaging (MRI) uses the nuclear magnetic resonance (NMR) phenomenon to produce images. When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B0), the individual magnetic moments of the spins in the tissue attempt to align with this polarizing field. If the substance, or tissue, is subjected to a magnetic field (excitation field B1) which is in the x-y plane and which is near the Larmor frequency, the net aligned moment, Mz, may be rotated, or “tipped”, into the x-y plane to produce a net transverse magnetic moment Mt. This excitation pulse is a radio frequency (RF) signal. A corresponding radio-frequency signal is emitted by the excited spins, and after the RF excitation signal Bl is terminated, this emitted signal may be received and processed to form an image.
When utilizing these signals to produce images, magnetic field gradients (Gx Gy and Gz) are employed. The fields may be applied in a programmed sequence of pulses of varying amplitude, phase, duration and relative timing with respect to each other and to RF excitation pulses. This is often called a pulse sequence. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which these gradients vary according to the particular localization method being used. Each measurement is referred to in the art as a “view” and the number of views determines the quality of the image. The resulting set of received NMR signals, or views, or k-space samples, are digitized and processed to reconstruct the image using one of many well known reconstruction techniques. The total scan time is determined in part by the length of each measurement cycle, or pulse sequence, and in part by the number of measurement cycles, or views, that are acquired for an image. There are many clinical applications where total scan time for an image of prescribed resolution and SNR is at a premium.
MR imaging of matter is based on the observation of the relaxation of the spins as measured by the amplitude of the emitted pulse that takes place after the RF pulse has stopped. The return of the excited nuclei from the high energy to the low energy state is associated with the loss of energy to the surrounding nuclei. Macroscopically, this spin-lattice or T1 relaxation is characterized by the return of the longitudinal net magnetization vector to a maximum length in the direction of the magnetic field. This return is an exponential process of the form of 1−e−t/T1. The T1 relaxation time is the time constant of this exponential: i.e. the time needed for the longitudinal magnetization to return to (1−1/e) of the original value.
Microscopically, T2 relaxation, or spin-spin relaxation, occurs when the spins in the high and low energy state exchange energy but do not loose energy to the surrounding lattice. Macroscopically, this results in a loss of transverse magnetization. T2 relaxation is also an exponential process, in the form of e−t/T2, and the T2 time is the time needed for the transverse magnetization to decay to 1/e of the original value. In pure water, the T2 and T1 times are approximately identical. For biological material, the T2 time is considerably shorter than the T1 time.
By varying imaging parameters such as TR (repetition time of the RF pulse) and TE (echo time interval of a spin-echo sequence), it is possible to weight the signal emitted by the tissue being imaged to produce T1-, T2- or PD-weighted (proton density) images. From a medical perspective, this means that MR imaging can provide multiple image contrasts, emphasizing different tissue features so as to observe the same anatomy. White matter would appear in a light grey in a T1-weighted image and a dark grey in a T2-weighted image. Grey matter would appear grey in both images. The cerebrospinal fluid (CSF) would appear as black in a T1 weighted image and white in a T2 weighted image. The background of the image (air) would appear as black in both images.
The echo time, TE, is the time from the first excitation RF pulse to the center of the echo (signal) being received. Where a spin-echo pulse sequence is used, the TE is the time interval between data measurements associated with the refocusing pulses and is much shorter than T2. Shorter echo times allow less T2 signal decay. The Repetition time, TR, is the time between RF pulses (not including the refocusing pulses). Short TR values do not allow the spins to recover their longitudinal magnetization, so the net magnetization available would be reduced, depending on the value of T1. A short TE and long TR give strong signals.
Diffusion Tensor MRI (DT-MRI) is a magnetic resonance (MR) imaging modality which is capable of non-invasively measuring the bulk diffusive motion of water in biological systems. These images are often called Diffusion Weighted (DW) images so as to differentiate the data from data taken with, for example, conventional T1 or T2 weighting.
The diffusion coefficient D (i.e. random motion of molecules in tissue) is larger in directions along structures in tissues (e.g. along nerve tracts or along muscle) than in directions perpendicular to the structures. That is, the diffusion could be anisotropic.
The diffusion coefficient may be mathematically characterized as a 3×3 second-rank tensor matrix. In diffusion tensor imaging, the diffusion properties of water are measured in a laboratory frame of reference, for example, using the spatial coordinates x, y, and z (where z is the axis along the main magnetic field B0 of the MR device). The tensor matrix has nine non-zero elements, of which three are the same (symmetric tensor). The remaining six elements (Dxx, Dyy, Dzz, Dxy, Dxz, and Dyz) for each voxel may be calculated from a minimum of six images which may be obtained by applying diffusion-sensitizing gradients in at least six non-colinear directions (for example: xx, yy, zz, xy, xz, and yz) in addition to a nondiffusion-weighted image. A property of second-rank tensors is that they can be diagonalized, leaving only three nonzero elements along the main diagonal of the tensor: the eigenvalues (λ1, λ2, λ3). The eigenvalues reflect the shape or configuration of the ellipsoid. The relationship between the principal coordinates of the ellipsoid represented by the diffusion tensor and the laboratory frame is described by the eigenvectors (v1, v2, v3).
In practice, the orientation of the gradient axes, which are determined by the physical architecture of the MRI device, are in a Cartesian reference frame (x, y, x), whereas the orientation of the tissue with respect to the reference frame is not generally known a priori.
When measurement noise, patient movement and equipment limitations are taken into account, a larger number of axial directions may be used to accumulate the measurement data. Between N=6 and at least 256 independent axes are known to have been used or theoretically evaluated. The use of a large number of measurement axes is often termed High Angular Resolution Diffusion Imaging (HARDI).
During random diffusion, the displacements of the molecules may serve to probe tissue structure on a microscopic scale; this resolution is well beyond the usual image volumetric resolution. During a typical diffusion time of about 50 ms, a water molecule, for example, may move an average distance of about 10 μm, interacting with many tissue components such as nerve fibers, cell membranes and the like. Thus, the overall effect observed in a DW MRI image of a voxel, which may be several mm3, may represent the statistical diffusion behavior of the water molecules within the voxel.
In particular, voxels containing neuron bundles exhibit significant anisotropies in the diffusion tensor, with the high-diffusion eigenvector being observed to be aligned with the nerve fiber bundle. The measured diffusion tensor may be used to define the local principal axis of a neuron or neuron bundle and then used to enable the identification of the orientation of nerve bundles with respect to each other and to other structures of the brain.
Fiber tracking simplifies the diffusion tensor field to the vector field of the main eigenvector. Conceptually, considering this vector field as a velocity field and dropping a free particle on it, this particle will follow a trajectory constrained by the velocity field. The resultant trajectory may be considered as representing a bundle of nerve fibers in the brain or muscle fibers. Fiber tracking shows global information about, for example, the connections between portions of the brain by neural tissue, and the orientation of these connections with respect to the surrounding organs and structures.
The diffusion data are determined in a magnetic resonance measurement as related to the magnitude and direction of the diffusion gradient fields used for diffusion coding. In an implementation, strong magnetic gradient pulses G are applied time-symmetrically about a 180° radio-frequency refocusing pulse in a spin-echo pulse sequence. The first gradient pulse, applied before the 180° refocusing pulse generates, a phase shift for all spins; and, the second gradient pulse, applied after the refocusing pulse, inverts the phase shift. Where the molecules are stationary during this time period, the phase shifts cancel. The water molecules may move due to Brownian motion, and their motion may be constrained by the tissues. For the molecules that, due to this diffusion, are located at a different location during the second gradient pulse from where they were located during the first gradient pulse, the phase shift may not be completely compensated. This leads to a reduction in amplitude of the magnetic resonance signal from the voxel, and the signal amplitude thus depends on the diffusion tensor (DT) of the voxel.
The diffusion weighting (DW) gradients are applied independently of the gradients used to encode the image data for acquisition of slice of MRI data. The degree of diffusion weighting is described by a parameter known as the “b value” or “b,” that is determined by the properties of the diffusion-sensitizing gradient scheme. For the Stejskal-Tanner spin-echo scheme (see, “Spin Echoes in the Presence of a Time-Dependent Field Gradient” by E. O. Stejskal and J. E. Tanner J. Chem. Phys. 42, 288 (1965)), for a pulsed pair of approximately rectangular gradients symmetrically disposed around a 180° radiofrequency pulse, the b value is determined by the duration (δ) and strength (G) of the sensitizing pulsed magnetic gradients, and the time interval between the two pulsed gradients (Δ) according to:b value=γ2G2δ(Δ−δ/3)  (1)where γ is the gyromagnetic ratio. Thus, the b-value (diffusion sensitization) can be increased by using stronger G and longer δ pulsed gradients, or by lengthening the time Δ. A typical value for b in human measurements is 500-2000 s (seconds)/mm2, but values in the range of about 0 to about 10,000 s/mm2 may be used. The signal intensity (S) in every voxel of a diffusion-weighted MR image is influenced by the choice of b value and pulse sequences and imaging parameters such as TE, and tissue specific apparent diffusion coefficient D, a coefficient that reflects molecular diffusivity in the presence of restrictions, such as viscosity and spatial barriers; and spin-spin relaxation time (T2).S=S0exp(−bD)  (2)where S0 is the signal intensity at a b value of 0.
Acquiring diffusion-weighted images with at least two different b values (for example, approximately 0 and 1000 s/mm2) while keeping the TE fixed allows the determination of the tensor D for each image voxel. Assigning a gray scale to the range of D values in the different voxels comprises a D map. The map provides contrast based purely on differences in diffusivity of water in biologic tissue that is not distorted by differences in T2 relaxation times.
DT-MRI may be used to study neuro-connectivity and neuron fibers for clinical diagnosis as well as for pre-surgery planning. For currently used diffusion tensor models a high b-value may be needed to identify and distinguish areas of fiber crossings. However, a short echo time TE is desirable so as to maximize the signal-to-noise ratio (SNR) as well as to detect tissues with shorter values of T2, such as muscle.
In practice, the gradient coil and gradient-coil-power amplifier sub-system of a MRI device has performance limits. As a consequence, a compromise between TE and the b-value is made in clinical practice. Where this is done, averaging of the signals for each voxel for a plurality of measurements may be needed to ensure a sufficient SNR to perform the subsequent analysis. This may result in an extended imaging time when High Resolution Radial Direction Imaging (HARDI) is performed.
One factor which may establish a lower bound on the value of TE may be the capability of the gradient power amplifier (GPA) of the MRI device when the diffusion gradient is aligned on one axis: e.g., xx, yy, or zz.